Pursley left following the conclusion of this summer's Games and Adlington said the swimmer had been "dying for them [British Swimming] to appoint a head coach for months".
The public outburst saw Sparkes offer a meeting to the 23-year-old from Mansfield where she could express her views to him personally and British Swimming has revealed the pair have now spoken to each other.
"British Swimming chief executive David Sparkes has held initial discussions with Olympic swimmer Becky Adlington to listen to concerns raised following this week's publication of the London 2012 Performance Debrief Report," said a British Swimming statement.
"A healthy debate took place where Sparkes listened to and responded to the issues raised by Becky in the media this week.
"Sparkes will now meet the British Swimming Athlete Leadership Group next month to update on actions from the Debrief report and to ensure enhanced two-way communication with the group."
The London 2012 Performance Debrief published this week claimed British Swimming did not need "radical" overhaul despite the Olympic failure.
At London 2012, Team GB claimed just three medals with the two bronzes from Adlington and a silver for Michael Jamieson to finish down on their target of five set by UK Sport.
The report from the debrief forced the resignation of national performance director Michael Scott after it recommended that he should be based permanently in the United Kingdom, rather than commuting from his home in Melbourne.
It also criticised Pursley – who had left before the report was published – by highlighting weaknesses in the sport's "technical and coaching leadership", but it concluded that no one single factor was responsible for Team GB failing to reach its target London 2012.
The recruitment process for a new national performance director and head coach are now underway, while Mark Perry, who led the open water and development programmes for British Swimming, has taken up the role of interim technical lead.
That move sees Graham Bassi, the current assistant coach at the British Gas Swansea Intensive Training Centre (ITC), replace Perry as the interim manager of the development programme, with British Swimming's director of world class operations Ian Mason becoming interim line manager to those who previously reported to Scott.
Contact the writer of this story at email@example.com
December 2012: Embattled British Swimming announce interim leadership appointments
December 2012: British Swimming does not need "radical" overhaul review into London 2012 concludes
November 2012: British Swimming performance director quits after he refuses to live in Britain
September 2012: Adlington surprised at being excluded from London 2012 review
September 2012: Phelps' coach to help British Swimming review into London 2012 disappointment